equi-marginal principle

What is Utility?

Utility is a way of measuring how much satisfaction or happiness a consumer gets from consuming goods or services. Think of it as a score on a happiness meter. The higher the score, the more you enjoy that item.

In economics we write it as a function: $U(x_1, x_2, \dots)$, where each $x_i$ is the quantity of a good.

Marginal Utility (MU)

Marginal Utility is the extra satisfaction you get from consuming one more unit of a good.

Mathematically: $MU_i = \frac{\partial U}{\partial x_i}$

Example: If you eat a slice of pizza, the first slice might give you a lot of joy ($MU$ high). The second slice might still be good but not as exciting, so its $MU$ is lower.

The Equi‑Marginal Principle (EMP)

When you have a fixed amount of money, the EMP tells you how to spend it so that your total utility is maximised.

It says: Spend your money until the last dollar spent on each good gives the same extra utility.

In formula form: $\frac{MU_1}{P_1} = \frac{MU_2}{P_2} = \dots$

Where $P_i$ is the price of good $i$.

A Simple Example

Imagine you have £10 to spend on two items:

• Chocolate bar (price £2)
• Apple (price £1)

Suppose the marginal utilities are:

Since $MU_{Apple}/P_{Apple} > MU_{Chocolate}/P_{Chocolate}$, you should buy more apples until the ratios equalise. This maximises your total happiness.

Exam Tip 🚀

1. Always check the marginal utility per pound for each good.
2. Show the equality condition: $\frac{MU_1}{P_1} = \frac{MU_2}{P_2}$.
3. Remember that if the ratio is higher for one good, you should buy more of that good.
4. Use a table to organise your calculations – it looks neat and helps you avoid mistakes.
5. Explain the logic in words: “The consumer allocates spending so that the last pound spent on each good gives the same extra satisfaction.”

Quick Recap

• Utility = happiness from goods.
• Marginal Utility = extra happiness from one more unit.
• Equi‑Marginal Principle = equalise $MU_i/P_i$ across all goods.
• Use tables and clear maths to show your reasoning.